Dynamic linkage between nifty-fifty and sectorial indices of national stock exchange

The main objective of this paper is to analyze the trend and pattern of the NiftyFifty and sectorial indices. An attempt has been also made to find out the causal relationship among the Nifty-Fifty and NSE sectorial Indices. The unit root test and Granger-causality test has been applied to check the causal relationship between Nifty-Fifty and sectorial indices. The finding of the study shows that the financial service sector had performed better and followed by the banking sector among all the indices while the Pharma sector and the Realty sector were Under-performed in comparison to other indices. The Nifty-Fifty has been found less volatile in comparison to other sectorial indices however Realty sector indices show the highest volatility during the study period.


Introduction
Published by "Global Research Network LLC" https://www.globalresearchnetwork.us maximum return with a minimum level of risk. Modern portfolio theory suggests that investors should construct a portfolio of multiple assets in order to get a maximum return at a given level of risk (Markowitz, 1952). The securities exchanges of developing economies have been of crucial significance to the worldwide speculation network. Since developing markets are more unstable than the very much created securities exchange, consequently, the developing markets will, in general, be disconnected from each other and with the created markets. Various financial specialists around the world selected to broaden their assets over the developing markets. Securities exchanges of developing economies have as of late been of fundamental significance to worldwide speculation network. The capitalization returns and instability have expanded significantly in these business sectors. Since developing markets are increasingly unstable than the very much created securities exchanges, along these lines, the developing markets will generally be inconsequential with each other and with the developed markets. In the practical context analysis of risk-return aspects, every company looks to be tremendous thanks to the necessity of a huge input file and massive time. With reference to the higher than constraints investors sometimes resort to index models for portfolio choice. Index models propose that the link between a set of securities will indirectly be measured by scrutiny of every security to a standard factor of 'market performance index' (Sharpe, 1963).
Sectoral linkage has turned into a discussed point in the portfolio creation process. The investors will, in general, make a portfolio by distributing funding to stocks from diverse sectors. Their allotment is simply subject to the execution and foreseen the development of the concerned sector.
The impact of the random walk can likewise impact the stock determination process. It refers that the investors will, in general, contribute with certain stocks dependent on great data from the concerned sector. Furthermore, they continue to amending their portfolio as per the availability of  Krishanmurty (2002), outlined the selection of econometric models for India, converse about some theoretical and empirical issues applicable to macro-modeling and the use of models in predicting, policy analysis and planning and, at last, set out the schedule for future work in the line. Objectives and methodology

Objectives of the study
This study has done to achieve the followings objectives:  To analyze the trend and pattern of Nifty-Fifty and sectorial indices.
 To compare the performance of Nifty-Fifty and sectorial indices.
 To examine the causal relationship between Nifty-Fifty and sectorial indices.

Hypotheses
 Null Hypothesis (H0): There is no significant relationship between Nifty-Fifty and sectorial indices.

Statistical tools used for analysis
The data has been analyzed with the help of various statistical tools like M-S Excel, E-Views and    We test properties of all indices series whether they are stationarity or not. If there are shocks present in the series then it will be non-stationary time series. Therefore, to identify the shock present in our data we need to apply Augmented Dickey-Fuller unit root tests (ADF Test). The null hypothesis supposed that the data series has a unit root or non-stationarity. Table 2 presents the results of the Augmented Dickey-Fuller unit root test for average daily return of Nifty-Fifty and other sectoral indices at level with constant only. The results indicate that the coefficient of lagged Nifty was negative. Also, its p-value was less than 0.05. This confirmed that the unit root test model was valid

Unit Root Test Results
and it was suitable to ascertain the stationarity of the data. The p-value of the Augmented Dickey-Fuller test was 0.00 for all the indices which were less than 0.05. So, we rejected the null hypothesis that the average daily return of Nifty-Fifty and other sectorial indices had unit root or non-stationery.
Hence, it was confirmed that data for the average daily return of Nifty-Fifty and other sectorial indices was stationary and it could be used for further analysis.

Results of Granger Causality Test
Granger (1969) proposed a time-series data-based approach in order to determine causality. Granger causality test shows the relationship of precedence among variables. This test will help in finding the answer to whether X causes Y. Y is said to be granger caused by X if X helps in the prediction of Y. It is applied to the stationary series. We take the null hypothesis as X doses not granger cause of Y and vice versa. Before applying to this test the optimal lag must be selected because the results are very sensitive to the number of lags used in the analysis. This study adopts the Schwartz information criterion (SIC) in which lag 4 is found to be the optimal lag for the total time periods.

Conclusion and suggestion
Stock market indices are calculated with references to a base period and a base index value.
Sectorial linkage has become a debated topic in the portfolio creation process so knowledge on sectoral inter-connection can play an important role in portfolio reallocation.